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Lagrangian Perturbation Theory : 3 rd order solutions for general dark energy models. Seokcheon Lee ( 이석천 ) Korea Institute for Advanced Study ( 고등과학원 ) Feb. 12 th . 2014 b ased on : arXiv /1401.2226. Outline. Why do we need LPT? Analytic Perturbation Theories

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lagrangian perturbation theory 3 rd order solutions for general dark energy models

Lagrangian Perturbation Theory: 3rd order solutions for general dark energy models

Seokcheon Lee (이석천)

Korea Institute for Advanced Study

(고등과학원)

Feb. 12th. 2014

based on : arXiv/1401.2226

outline
Outline
  • Why do we need LPT?
  • Analytic Perturbation Theories
    • Standard Perturbation Theory (SPT)
    • Lagrangian Perturbation Theory (LPT)
  • Application
    • Matter power spectrum
    • Two point correlation function
  • Third order solutions for general DE models
  • Future works
why do we need lpt
Why do we need LPT?
  • Upcoming large-scale surveys (LSST & Euclid) requireshuge number of mock catalogs to estimate covariance matrix
  • N-body simulations : accurate, numerically expensive
  • Semi-analytic methods (PThalos, PINOCCHIO, COLAR) : fast, inaccurate : using LPT to displace particles at large scales
analytic perturbation theories standard perturbation theory spt
Analytic Perturbation TheoriesStandard Perturbation Theory (SPT)
  • Both background evolution and perturbed quantities are required to study Large scale structure (LSS)
  • Linear theory well describes LSS in linear regime
spt ii
SPT II
  • There’s no reason to stop at linear order
  • Problems : convergences of an expansion are not clear, diverge at large k (cannot do FT), confined in real space
lagrangian perturbation theory lpt
Lagrangian Perturbation Theory (LPT)
  • In LPT, a fundamental variable to represent perturbation is a displacement field, S
  • First order LPT : Zel’dovich approximation
  • Initial conditions for N-body simulations are open generated using ZA or 2nd order LPT
  • LPT can overcome problems of SPT
lpt ii
LPT II
  • Drawbacks of LPT
    • Successful at high redshifts but poor results at late times due to shell crossing
    • Power in small scales is suppressed
    • Multiple streams through same Eulerian position
    • Before shell crossing, the system described by a velocity field
applications
Applications
  • Predictions for cosmological dependence (including Ωm ,ω, etc) on
    • (quasi-linear) power spectrum
    • Weak lensing
    • Bispectrum
    • Halo bias
    • Two point correlation function (BAO)
third order solutions for general dark energy models
Third order solutions: for general dark energy models
  • Goal
    • So far one uses EdS universe approximation for the time dependence part of solutions
    • Thus, one investigates 2pt CF or PS for ΛCDM model with this assumption
    • This is self inconsistent and can’t be used for the cosmological model different from ΛCDM
    • One needs to improve this in order to predict DE dependence on those observable
future works
Future works
  • Adopt the correct higher order solutions to power spectrum (in progress)
  • Using these solutions in the 2pt correlation function to forecast BAO signals (in progress)
  • Also check the prediction for WL